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You can read about many things here: from math to physics to earth science and biology, computer science and the technologies of today and tomorrow—but in general, centered around the theme of what scientists, engineers and programmers can do to help save a planet in crisis.

Feel free to ask questions or continue discussion on the many blog articles—it’s never too late! Or, if you have general questions about this blog or the Azimuth Project, please ask them here.

David MacKay (David JC MacKay FRS / Professor of Natural Philosophy, / Department of Physics, / University of Cambridge) has a good extensive analysis of ‘Sustainable Energy’ at http://www.withouthotair.com/

He is infact talking about information theory and sustainable energy at ICML (international conference on machine learning) at 14:00 today (28 June 2012) – http://icml.cc/2012/invited-talks/ sorry this reply is sort of out of synch. But maybe this will get read by those on the blog anyway.

I’ve been thinking about joining or creating an social network expert commnity-driven site for some time now and as I’ve followed your writings for some time I also decided to instead put my efforts on Azimuth which is the closest to what i had envisioned so far. So I’ll be able to dedicate my efforts towards Azimuth instead. I’ll join and see what is in the pipeline on the site or you might inform me what is prioritized.

Great! I’d love it if you’d join the Azimuth Project. I see you’ve become a member of the Forum — good start!

Right now the top-priority projects seem to be:

• Working through some well-known plans of action — strategies for dealing with global warming — and summarizing them, discussing them here on the blog, critiquing them, and eventually maybe trying to formulate our own.

• Making it easier for scientists, engineering and computer people to understand climate models.

There are also a lot of other projects to do, and I think it’s good for everyone to work on things that are fun and take advantage of their special skills.

I’m not sure if I’m going about this correctly but if not, please accept my apologies.

I wrote a blog explaining how greenhouse gases cause the stratosphere to cool. Here I offer a summary:

Temperature is a measurement of the translational Kinetic Energy (KE) of the particles. When CO2 and other particles collide with each other, some of the translational KE is converted into vibrational KE of the CO2. The loss of translational KE lowers the temperature and thus excites the CO2 molecules.

Nature prefers the lowest energy state and the excited CO2 molecules give up the vibrational Kinetic Energy by returning to the unexcited ground state. In so doing, they emit Infrared radiation. In the rarefied atmosphere of the stratosphere, this radiation does not impinge on stratospheric particles and simply escapes into space.

If the CO2 level of the stratosphere increases, there are more of these reactions and the temperature is lowered.

nothing to do with the climate, but I remember you were interested by the Voynich manuscript, so just in case you didn’t see the news: it has finally been carbon-dated, and was written between 1404 and 1438 (so about a century later than expected) http://uanews.org/node/37825

The easiest programs to write are educational: I used some to help explain issues in week308 and week309, and I plan to do more of that. One of the more exciting projects of this sort would be to develop models of the glacial cycles and how they might be caused by variations in the Earth’s orbital parameters. I have the data, I have the math, I just need someone to write the programs!

You can also see ideas for more ambitious projects that might have a bigger impact.

Staffan Lilgeren is also interested in writing simple climate models to study the effect of variations in the Earth’s orbit on glacial cycles. But I don’t know how much he’s done yet.

The project has a number of aspects, so there’s surely enough work to keep us all busy—the more of us, the merrier! But, it would be nice to coordinate a bit, so we don’t have two people doing the same thing.

I explained some details on the Azimuth Forum, and said that I’d love to discuss things and answer questions if I can.

The instructions for joining the Azimuth Forum look a bit long—but that’s just because I spelled them out in so much detail that even idiots like me could follow them, step by step. It doesn’t take long at all, except waiting for me to wake up (I’m in Singapore, I guess you’re on the other side of the world) and approve your application.

On this weblog people often ask “Where’s the beef” with regard to a lot of the topics that get bandied about here … so now we know – and we’ll send them your way. I hope you don’t have a beef with that.

Hi John. Congratulations on a brave decision. I agree completely with what you say in your introduction to your new blog, and I shall be following it with interest. We were in Singapore recently and met one of my former (undergraduate) students, who is now a Minister of Finance there – she talked a lot about sustainability.

Intriguing subject, octonions. The 8X8 matrix field shows up in connecting the nucleotides of the genetic code, and the hexagram logic of the I Ching. Is the mathematic/vector space of Octonions applicable to these other 8X8 fields? Some aspect of deep quantum string reality that resonates at different levels?

I note with some interest that you will be attending Macquarie University in Sydney to give a lecture, and that I will be attending.

These updates you send me regularly are quite interesting and I take the time to forward them to my father in the Graduate School of the Environment.

I was not initially aware that you were a mathematical physicist, but now that I am, I may have something that might interest you. Are you familiar with the field of time optimal quantum control a.k.a. Time Dependent Quantum Mechanics?

Unfortunately for me it seems to be a somewhat sensitive topic (think the War of the Currents on a nanoscale) and it has proved to be quite impossible to find a PhD scholarship in Australia in this area. Do you know of anybody who would be interested?

Anyhow, links to my master’s research on time optimisation is contained at http://www.quantumcontrol.wikidot.com/start free to distribute and copy. Let me know if you can help me with my concerns. All I dream of is a time optimal computer!

Look forward to hearing from you. My father and I disagree on the whole Elsevier issue (he’s with them and Springer, I’m a “free-to-all” kind of guy!), we are always debating the best way of disseminating information.

Hi! There are lot of people working on quantum control at Australia National University—see this—so if you can’t get a Ph.D. scholarship in that area there, I’m not sure where to suggest. I don’t work on it myself, but you might look at the CQT website and see if anyone there does.

I’ll actually be giving three talks at Macquarie starting tomorrow. First I’ll be giving the Mathematics Colloquium at 1 pm Monday 6 February 2012, in E7B T2:

Some ideas from quantum theory are just beginning to percolate back to classical probability theory. For example, there is a widely used and successful theory of “chemical reaction networks”, which describes the interactions of molecules in a stochastic rather than quantum way. If we look at it from the perspective of quantum theory, this turns out to involve creation and annihilation operators, coherent states and other well-known ideas – but with a few big differences. The stochastic analogue of quantum field theory is also used in population biology, and here the connection is well-known. But what does it mean to treat wolves as identical bosons?

Our heavy reliance on fossil fuels is causing two serious problems: global warming, and the decline of cheaply available oil reserves. Unfortunately the second problem will not cancel out the first. Each one individually seems extremely hard to solve, and taken together they demand a major worldwide effort starting now. After an overview of these problems, we turn to the question: what can we do about them?

Finally, Wednesday the 8th at 2 pm in E7A 333, after lunch with the category theorists, I’ll be giving this talk in the Australian Category Seminar:

Symmetric Monoidal Categories in Chemistry and Biology

Chemists use “chemical reaction networks” to describe interactions between things of different types. In population biology and the study of infectious diseases, “stochastic Petri nets” are sometimes used for the same purpose. In fact chemical reaction networks and stochastic Petri nets are essentially the same thing. The theory of symmetric monoidal categories can help us understand what this thing is, and how to work with it.

Unfortunately for everyone involved, especially ANU, they only study closed loop control, whereas I am focused on open loop control (time optimal, no feedback).

My PhD application, while impeccable in my eyes, had sufficient “inconsistency” for them to can the whole project. I have literally run through an exhaustive search of all Australian prospective supervisors, and none will touch a project that proposes time dependent matrix control.

It’s hard not to see jealousy in those academic eyes.

(Time taken)x(Energy Invested)= a constant

At best; and often a whole lot worse, provably for a closed loop control. Why would you bother with an adiabatic computer when you could do things time optimally?

In my advice for young scientists, one thing I hint at but don’t quite emphasize enough is that it’s wise to pick an advisor because they’re smart, well-connected, friendly, help their students get jobs, and do interesting work. And then, after you pick one, work on what they’re interested in. You can’t expect a supervisor to switch over to thinking about what you’re interested in: they’re the boss in this situation. There’s no point in feeling angry or rebellious about this. A Ph.D. is an apprenticeship, after all: it’s good to take advantage of that rather than fight against it. Once you get a degree, then it’s a good time to pursue your own research agenda.

Can you, or your supplier, do something about those meaningless times on comments? Without an indication of offset from GMT, they cannot be understood. Also, in an international medium, the 24-hour clock is better – those who do not understand it need to learn.

This will be sent at about 10:05 local, 09:05 GMT; we’ll see what you put.

I can’t get it to say “GMT” or “UTC”. I perhaps suboptimally chose the DD-MM-YYYY format for dates of news articles referred to on the Azimuth Wiki, so I’m using that too here. I apologize for my suboptimality.

You must know about this since Barry Brooks blog appears on your blogroll list but to anyone interested he wrote a series of reports on renewables called TCASE (Thinking Critically About Sustainable Energy)

I’d like to introduce you to some ideas and sources you might not be aware of, related to the issue you’re grappling with: how you should personally respond to anthropogenic climate change. The most important of these is antihumanism.

Antihumanism is a relatively new philosophy, which emerged along with critique of industrialism in the modern era, particularly after WWI. Antihumanism gathered strength from the nihilism of post-1960s counterculture and is now evolving rapidly, so there’s already a wide spectrum. At the moderate end are mainstream novelists such as Kurt Vonnegut (“Breakfast of Champions”), Margaret Atwood (“Oryx and Crake”), and Paul Theroux (“O-Zone”). All of these books contain antihuman concepts and observations, though their authors probably wouldn’t use the word. There are also many antihuman movies, too many to list, but at a minimum “Eraserhead” by David Lynch, “THX-1138″ by George Lucas, and “Soylent Green” should be mentioned. At the extreme end are actual organizations such as The Church of Euthanasia, VHEMT (Voluntary Human Extinction Movement), and GLF (Gaia Liberation Front).

In the sciences antihumanism is usually expressed by paleontologists and biologists, and increasingly by climate scientists. Some current examples are Jeremy Jackson and Kevin Anderson (see links below). Edward O. Wilson is best known for his work on biological diversity, but he was also the first biologist to seriously propose that intelligence snuffs itself out, and that this solves Fermi’s paradox: we don’t receive messages from the stars because by the time an alien life form has enough power to transmit that far, it’s already on the threshold of annihilating itself, and the odds of its brief blaze of glory lining up with ours are infinitesimal. This is closely related to the view that life (particularly human life) creates short-term order at the cost of accelerating the entropy of its environment, in stark contrast to the idealistic Gaia theory. For example paleontologist Peter Ward’s “Medea Hypothesis” demolishes the notion that life is self-regulating, and compares life to a drunk stumbling around in a darkened room.

Antihumanism can be usefully contrasted with humanism. Humanism derives from the ancient Greek notion that man is the measure of all things, and that without human existence nothing would have value. Concealed within this is the assumption that only humans experience value. This assumption has no basis in biology, but is nonetheless one of the pillars of modern civilization, because it provides justification for extermination of other species. The denial of intrinsic value to non-human life is the essence of speciesism, and is closely related to the dogma of dominion, i.e. that it’s man’s destiny to subjugate all other living things (a concept that Edward O. Wilson attacked in his “Consilience”).

Beyond humanism is transhumanism, sometimes known as futurism or extropianism. This is the belief that not only is man the measure of all things, but the only part of him that matters is his mind, and the sooner his mind is freed from the limitations of biology the better. The moderate form is life extension and cryogenics, while the extreme form is downloading human intelligence into robots and conquering outer space, like the Daleks on Dr. Who. Famous transhumanists include Ray Kurzweil, and Stephen Hawking who recently stated that humanity’s only hope is to escape to other planets before we destroy this one. Antihumanists regard transhumanists as archenemies due to their flagrant disregard for non-humans. From the antihuman point of view, transhumanism bears a striking resemblance to Christianity. Both are escapist, characterized by unshakable belief that humans belong somewhere else, i.e. Heaven/Outer Space. Both express hatred for biology, e.g. Catholic repression of sexuality, and transhumanist use of derogatory terms such meatspace. Both are motivated by fear of death, and presumably of life too, since one engenders the other (literally via natural selection). Both reject the limits of existence on earth, and promulgate a fantasy that justifies exceeding those limits. The danger isn’t that the fantasy will be realized, but that deluded people will make earth unsuitable for life far sooner than would have otherwise been the case.

Unlike mere misanthropy, antihumanism is distinguished by reverence for non-human life. Biological diversity is considered an axiomatic value, and contrasted with the ugliness and sterility of human monoculture. Earth is described as a “wrecked planet” (Kurt Vonnegut), and various measures are called for to prevent further damage, the most obvious being drastic reduction or elimination of the human population. The pre-human fecundity of earth is idolized, and provides a reference for demonstrating impoverishment of ecosystems. This relates to the shifting baseline syndrome posited by Jeremy Jackson and others, in which each successive generation incorrectly assumes the degree of biological diversity they observe was also seen in previous generations.

The central paradox of antihumanism is that humans evolved, and are arguably no more or less natural than any other living thing. Stephen Jay Gould argued convincingly that evolution doesn’t converge on anything except fitness for conditions: there are no good or bad organisms, just ones that survive, and mostly ones that don’t. Richard Dawkins went even further and described organisms as mere transport for genes, in which case the DNA we share with all other eukaryotes is the winner, regardless of what humans do. One proposed resolution is that humans are malignant life, as argued by A. Kent MacDougall in “Humans As Cancer”. This sidesteps the problem however, because cancer is also natural, and is closely related to viruses. The higher-order question is ethical: why is malignancy bad, and from what point of view is its badness determined?

The paradox of human naturalness could possibly be resolved by arguing that sentience is not intelligence but the ability to feel pain and pleasure. What distinguishes humans from other primates is the existential suffering that results from self-knowledge, particularly fear of death. Since humans have such capacity for suffering, we should have equally developed empathy, but instead we succumb to corruption, creating hellish conditions for humans and non-humans alike. Thus despite our naturalness, humans can and should be blamed for wrecking the planet, precisely because we’re capable of feeling remorse for having done so. If we’re unable to reform ourselves, as seems increasingly to be the case, we should have the decency to step aside and give other organisms a chance. Apes might re-evolve back into us, but they might not, and either way it won’t be our fault.

Interesting. Cancer is a pretty good analogy for civilisation I think. Not for humanity as such, but specifically civilisation, where humans create cities and practise agriculture. Part of a system growing ‘exponentially’ for the sake of growth itself, and consuming resources without regard for the whole. Also, if you look at a photograph of a grey, necrotising cancer tumour embedded within healthy pink tissue, and then at a photograph of a grey city embedded within a healthy green environment and ‘squint’ a bit, they do look strikingly similar (if you allow for a shift from green chlorophyll to red haemoglobin), …right down to the development patterns along arterial routes. You can even see ‘metastasis’ happening in the form of colonisation along trade routes. The same pattern of overconsumption being propagated remotely as well as locally.

Whilst I share the view that natural biodiversity, complexity and beauty are absolute goods or values, which deserve admiration, respect and protection irrespective of human purposes and benefits, and whilst I also share a certain ‘pessimism’ about human nature and the chances of averting massive ‘ecocide’ (..and further, I would say that the world human population should be reduced gradually but very considerably to about the population density of Canada or Australia or Sweden) …I am still very much a fan of humanity as a species.

I think we are in a collective mental rut though and desperately need some new models.

As far as I can see, the only way to change an outmoded model (or underlying, behaviour-driving belief system?) is to thoroughly examine the model in its entirely and in its full complexity, thus revealing its inner contradictions, its over-simplifications, its limits of applicability, etc. I don’t think that process can be short-circuited. (I mean there is no short-cut. Human history is littered with attempts to change things without understanding them first and that hasn’t worked.) The difference between internally coherent, ‘responsible’ (responsive to the needs of the whole system) models, and internally incoherent and irresponsible models, is that the former can withstand thorough scrutiny and the latter cannot. This difference can perhaps be exploited in the same way that the difference between normal cells and cancer cells can be exploited with chemotherapy (…in that normal cells retain the ability to repair DNA damage caused by chemotherapy drugs and cancer cells do not.)

I appreciate your work and share your thinking on what the planet needs. I was looking for your notes on economics but the link on your website does not work. Is there a way I can find those? I would be interested to read your view on that.

Thanks for the link; this is what I was looking for. I appreciate your efforts by talking about what scientists can do to help the planet. I am also of the opinion that the problem lies at the heart of how governments frame policies that, in turn, shape the world. The classical economic model of ‘wealth maximization’ needs to be replaced with policies that support resource sustainability rather than unnatural growth fueled by liquidity and debt. Sensible policies would allow a natural balance between the environment and economic prosperity. By framing the policies with just one objective in mind (growth), we have created a state of artificial demand that has resulted in the current mess.

Nature has a mechanism to keep things in balance. With the establishment of the current socio-economic system, the planet does not have a natural way to control human population.The false sense of economic prosperity and wealth creation portrayed by aggressive expansionary economic policies have allowed the human population to burgeon. It is imperative that we think of the restrictions on the supply side. The governments have allowed expansionary policies over years to create the situation we face today. In my view, economic policies should aid resource sustainability instead of focusing on perennial growth – the main reason why the planet is in danger today. By promoting policies that keep a check on exploitation of resources, the governments could help keep an implicit check on global population. The idea may sound offbeat but there is a remote chance of improvement until the officials take the lead.

I agree that we need to slow the exploitation of resources, but most governments are set on doing the exact opposite. So, the trick is to figure out how to persuade governments to change their policies. Replacing GDP with some sort of ‘genuine progress indicator’ might help. That’s why we have this page:

However, it seems to work when I check now. Maybe I encountered a technical problem then.

Regarding ‘Genuine Progress Indicator’, it’s a good concept but it may not work on a standalone basis. GDP incentivizes investors to provide funds and this reduces the cost of capital, pushing up asset prices. Genuine Progress Indicator may deduct various costs from the GDP but these are intangible in nature; the investors may discount these and the net effect would be marginal. I think such an index needs to be supplemented with a shift in the taxing policies to restrict activities hazardous to nature.

I visit your blog twice a week and I intend to continue doing so. I hope you continue with your commendable work and I look forward to learning more about your views.

I have been enjoying reading through your blog posts on topical developments in physics, and will take up perusing posts on other topics of interest here as well when I can.

With the publication of the WMAP data, and now, the fantastic results obtained in the Planck project, a question has come to mind that I have not seemed to be able to find an answer to.

It is, of course, the case that all the data we receive about the universe and the state of matter within it is through the detection of EM radiation (light). It is my understanding that our insight into the physical significance of this data is necessarily governed by the model of the universe we use to interprete the data.

The question that comes to mind, for which I have yet to find an answer (google search and all), is: Has there ever been an attempt to perform a model independent experiment to calibrate the propagation of light over cosmologically relevant distances?

My understanding is that the luminosity-distance correlations, (and other methods for establishing distance relationships of celestial objects assume that light propagates across large distances (in an unobstructed field free static space), according to a metric that is Minkowskian. But, I cannot seem to find any information about any empirical experiment to verify that this assumption is correct.

I am hoping that you can point me to where I can find information on what our current state of knowledge is on this subject, and more particularly, any results obtained from model independant empirical experiments that confirm .

In reading through all the newly published papers produced by the researchers working on the Planck project and the stunning findings they have reported, the notion of asking, at this late date, if anyone has ever undertaken an experiment capable of “calibrating” how light propagates over great distances carries with it a note of some wonderment.

One would think, if it has not already been done, that the results of an empirical test which would be the physical “analog” of the Michelson-Morley experiment* on an astronomical scale, or some other model independant test that would directly calibrate how light propagates over cosmologically relevant distances, would be of compelling interest to astronomers, astrophysicists and cosmologists, and that it would be a matter of some priority to establish.

Thank you again for Azimuth. Its a great resource and a huge service for those of us who are interested in ideas about the “world” we live in.

Andrew

* I refer to the M-M experiment losely. But the concept I hope is illustrative of the idea of conducting an experiment to determine whether light traveling over great distances would produce data that would give a null result in the M-M experimental model.

[…] scientists, engineers and programmers trying to help save the planet. On the Azimuth Wiki and Azimuth Blog we are trying to explain the main environmental and energy problems the world faces today. We are […]

As I’ve mentioned previously, one of the amazing features of the internet is that you can take almost any idea and find a community obsessed with it. Thus, it isn’t surprising that there is a prominent subculture that fetishizes rationality and Bayesian learning. They tend to accumulate around forums with promising titles like OvercomingBias and Less Wrong. Since these communities like to stay abreast with science, they often offer evolutionary justifications for why humans might be Bayesian learners and claim a “perfect Bayesian reasoner as a fixed point of Darwinian evolution”. This lets them side-stepped observed non-Bayesian behavior in humans, by saying that we are evolving towards, but haven’t yet reached this (potentially unreachable, but approximable) fixed point. Unfortunately, even the fixed-point argument is naive of critiques like the Simpson-Baldwin effect.

For a topic, I would love to see you guys do a book review of this book. I thought he put a lot forward with his account of the second law applied to cosmology which I found very accessable and well presented. He points out some inconsistancies of existing mainstream theory that I thought were fascinating. But overall just a really cool geometry of the universe that I thought I would share with your blog.

I’m glad you’re eager to help! One way to get started is to join the Azimuth Forum, where we talk about what we’re doing. You can do this by clicking the link and following the directions, which look more complicated than they are. Please choose your real name as username.

David Tweed also has experience in machine learning and he is interested in simple ways of trying to understand global warming, which do not use detailed global climate models. This is a bit similar to what the Berkeley Earth project is doing.

We have a number of computer-related projects underway which you can read about here. Unfortunately we are moving rather slowly on these.

But we are also doing lots of other things. You can look at the Azimuth Forum even before you join it, to see what some of these are.

Dear John Baez,
I continue to find your posts inspiring, and I would like to share with you the completion of the first stage of my harmonograph-as-a-work-of-art project, documented on my new site anitachowdry.com. Here is a page of drawings that the beast has produced : http://www.anitachowdry.com/iron-genie-drawings/4582085804 I couldn’t begin to describe the maths in them, but they do inspire me with an almost Pythagorean sense of awe.
The machine is now ready to be loaned/hired out for for public appearances, so if anyone has any ideas about institutions that would like to have it for a period of public engagement, I would be most interested to hear from them.
I hope you enjoy the Iron Genie beast, Anita

Nice pictures, Anita! Let me post a little one here so people are tempted to visit your site:

I have another blog, Visual Insight, which is about explaining math through beautiful images. I’m tempted to ask you for a nice image made by your harmonograph! The problem is that without a detailed description of how the machine works, I can’t figure out the physics, and then the mathematics, that lurks beneath the beautiful surface of these images.

I hope you’ve been enjoying the nice pictures of rolling motions created by Greg Egan and others… the pentagram of Venus is reminiscent of your harmonograph patterns, and probably related, mathematically speaking.

I will try to think about institutions that might like the harmonograph. Does it need a trained person to operate it? Does it need you?

By the way, I’ll be in Oxford from February 21 to March 14, visiting the computer science department. I’m afraid I won’t have the time to go into London, though…

Anita, I was intrigued by your posts a few months back describing your plans for the harmonograph, and am very pleased to see this machine has been brought into being! It’s quite beautiful — really the most elegant harmonograph I’ve seen (and of course its products are fascinating as well). Congratulations!

I had mentioned your name (and sent a link to your blog) to an artist who lives in my town, Jane Philbrick, who is also intrigued by the idea of bringing mathematics and visual art together. One of her recent projects involved the re-creation of a sculpture (Marta Pan’s Sculpture Flottante I) into different media, including sound waves. The rough idea here, as I understand it, was to represent the characteristic sound forms of the sculpture (cf. “can one hear the shape of a drum?”) mathematically, and then render this representation sonically, to suggest possible “evolutions” of the shape (which were finally compiled into a sculptural “swan song”). This also wound up being the basis of a mathematics paper on the arXiv, which John might find intriguing as well. Curious stuff!

Dear Todd, Thankyou for your kind comments – very gratifying! Jane Philbrick’s work sounds intriguing, and reminds me of another collaborative project by a French artist called Anais Tondeur (visualizing the sound of graphite).

The movement of collaborations between artist and scientists keeps gaining greater momentum, and I think it very fruitful – in fact many of last year’s new intake on the Central Saint Martin’s M.A. Art & Science had scientific – mostly biological or earth sciences – (& not art) training – so the boundaries are ever more blurred. In fact, I tend to think that maths is in many ways an arts/philosophy discipline.

In this respect I am very grateful to John Baez for providing such a lively platform for sharing and discussing such ideas.

Many thanks for your interesting reply John, with so many suggestions. Just clicked through to Visual insight – thanks for pointing me to that , I intend to browse in more detail.
I would be very happy to give you as many images as you wish.

John Martineau, founder & director of Wooden Books http://www.woodenbooks.com/ came & had a look at it and explained how to count the beats of the pendula with a stopwatch to get approximate ratios that create distinctive classes of drawings, so I can try & make notes with the next batch. But unlike a computer programme, the Genie is full of crazy unpredictable variables!

Not much training required for the Iron Genie – the whole point is that audiences can have fun making the drawings themselves – I just watch & explain initially what to move. An intern could even help with that. (That’s why I had a young girl demonstrating in the video)

I am delighted to hear that you will be visiting Oxford – I can come & see you if you have time for a drink. If that is a possibility could you e-mail me?

I assume so, but you’ll have to ask the blog administration for more info; I’m just posting for them because they sounded like they needed scientific contributors and I thought you guys might be interested.

John, I have a chapter, no. 5, of an eBook called Superexponential algebra being written up on my website, which is in violation of the ‘non-existence of elements of Hopf invariant one’, and I was wondering if you would like to comment on it, since you have written on division algebras?

How To Write Math Here:

You need the word 'latex' right after the first dollar sign, and it needs a space after it. Double dollar signs don't work, and other limitations apply, some described here. You can't preview comments here, but I'm happy to fix errors.